Related papers: Jordan blocks and the Bethe ansatz III: Class 5 mo…
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…
We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible…
Jordanian deformations offer rare integrable realisations of non-AdS holography, whose solvability methods differ from conventional AdS/CFT examples. Here we study the $\mathfrak{sl}(2,R)$ sector of the Jordanian deformed $AdS_5\times S^5$…
In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential $V(q)$, $q\in\C^n$, of degree $k\in\Z^\star$. The known results of Morales and Ramis give necessary conditions for the complete integrability of…
It was recently suggested -- based on general self-consistency arguments as well as results from the bootstrap (arXiv:2005.07708, arXiv:2007.11539, arXiv:2007.04190) -- that the CFT describing the $Q$-state Potts model is logarithmic for…
A special class of Jordan algebras over a field $F$ of characteristic zero is considered. Such an algebra consists of an $r$-dimensional subspace of the vector space of all square matrices of a fixed order $n$ over $F$. It contains the…
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…
The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz technique. From the properties of the algebra generated by the local jump operators, we explicitly construct the hierarchy of…
For a conjugation $C$ on a separable, complex Hilbert space $\mathcal{H}$, the set $\mathcal{S}_C$ of $C$-symmetric operators on $\mathcal{H}$ forms a weakly closed, selfadjoint, Jordan operator algebra. In this paper we study…
The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld…
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called…
The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted…
These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian…
In this work we diagonalize the double-row transfer matrix of the supersymmetric t-J model with non-diagonal boundary terms by means of the algebraic Bethe ansatz. The corresponding reflection equations are studied and two distinct classes…
We study the Gaudin models associated with $\mathfrak{gl}(1|1)$. We give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation $\mathfrak{gl}(1|1)[t]$-modules. It…
We study the anomalous dimensions of operators in the scalar sector of \beta-deformed ABJ(M) theories. We show that the anomalous dimension matrix at two-loop order gives an integrable Hamiltonian acting on an alternating SU(4) spin chain…
In this paper, we calculate the Jordan decomposition (or say, the Jordan canonical form) for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix being a Jordan block and the diffusion coefficient matrix…
The Euclidean action with acceleration has been analyzed in [1], hereafter cited as reference I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian…
This is a transcription of a conference proceedings from 1985. It reviews the Jordan algebra formulation of quantum mechanics. A possible novelty is the discussion of time evolution; the associator takes over the role of $i$ times the…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…